Remeshing and eigenvalue stabilization in the finite cell method for structures undergoing large elastoplastic deformations

• Published in: Archive of applied mechanics (1991) Vol. 94; no. 9; pp. 2745 - 2768
• Main Authors: Sartorti, Roman, Garhuom, Wadhah, Düster, Alexander
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2024; Springer Nature B.V
• Subjects: Classical Mechanics; Deformation effects; Eigenvalues; Elastoplasticity; Engineering; Iterative solution; Original; Radial basis function; Stabilization; Stiffness matrix; Strain analysis; Theoretical and Applied Mechanics; Finite strains; Finite cell method; Data transfer; Remeshing; Elastoplasticity; Stabilization
• ISSN: 0939-1533; 1432-0681
• DOI: 10.1007/s00419-024-02644-z

Large strain analysis is a challenging task, especially in fictitious or immersed boundary domain methods, since badly broken elements/cells can lead to an ill-conditioned global tangent stiffness matrix, resulting in convergence problems of the incremental/iterative solution approach. In this work, the finite cell method is employed as a fictitious domain approach, in conjunction with an eigenvalue stabilization technique, to ensure the stability of the solution procedure. Additionally, a remeshing strategy is applied to accommodate highly deformed configurations of the geometry. Radial basis functions and inverse distance weighting interpolation schemes are utilized to map the displacement gradient and internal variables between the old and new meshes during the remeshing process. For the first time, we demonstrate the effectiveness of the remeshing approach using various numerical examples in the context of finite strain elastoplasticity.